Interpret the given powers

• Spectacles for distant vision: power $P_1=-1.0\,\text{D}$
• Reading glass: power $P_2=+2.0\,\text{D}$

Find the far point of the eye

Since the person uses spectacles of power $-1.0\,\text{D}$ for distant vision, this is a myopic eye.

For distant objects $(u=\infty)$, the correcting lens must form the image at the person's far point.

Focal length of the spectacles: $f_1=\frac{1}{P_1}=\frac{1}{-1.0}=-1\,\text{m}$

Hence the far point of the unaided eye is at $R=1\,\text{m}$

Use the reading glass information

The reading glass has power $P_2=+2.0\,\text{D} \Rightarrow f_2=\frac{1}{2}=0.5\,\text{m}=50\,\text{cm}$

A reading glass is used so that an object placed at the least distance of distinct vision $D$ of the defective eye forms a virtual image at the normal reading distance $25\,\text{cm}$, or equivalently, the given added power tells us the eye lacks accommodation corresponding to $2.0\,\text{D}$

For a person whose far point is at $1\,\text{m}$, the accommodation needed to see an object at distance $D$ is $\frac{1}{D}-\frac{1}{R}$

The reading glass of power $2\,\text{D}$ compensates this deficiency, so $\frac{1}{D}-\frac{1}{1}=2$

Therefore, $\frac{1}{D}=3$ $D=\frac{1}{3}\,\text{m}=33.3\,\text{cm}$

But this does not match any exact option, so let us use the standard interpretation for such JEE-style questions:

Standard near-point correction relation

The eye is corrected for distance by the $-1\,\text{D}$ lens, so its far point is $1\,\text{m}$.

The reading glasses of power $+2\,\text{D}$ are used to make an object at the normal least distance of distinct vision $(25\,\text{cm})$ appear at the person's actual near point $D$.

For the reading glass:

• object at $u=-25\,\text{cm}$
• virtual image at $v=-D$
• focal length $f=+50\,\text{cm}$

Using lens formula: $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ $\frac{1}{50}=\frac{1}{-D}-\frac{1}{-25}$ $\frac{1}{50}=-\frac{1}{D}+\frac{1}{25}$ $\frac{1}{D}=\frac{1}{25}-\frac{1}{50}=\frac{1}{50}$

Hence, $D=50\,\text{cm}$

Check options

• A: $50\,\text{cm}$ ✅
• B: $40\,\text{cm}$ ❌
• C: $30\,\text{cm}$ ❌
• D: $10\,\text{cm}$ ❌

Final answer

The least distance of distinct vision for this person is $\boxed{50\,\text{cm}}$